Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x + 2$ and $ KL = 6x - 5$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x + 2} = {6x - 5}$ Solve for $x$ $ -x = -7$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({7}) + 2$ $ KL = 6({7}) - 5$ $ JK = 35 + 2$ $ KL = 42 - 5$ $ JK = 37$ $ KL = 37$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {37} + {37}$ $ JL = 74$